Why so? How well-defined? I find it useful to base normative epistemic arguments off of the existence of Chaitin’s omega, even though there isn’t a unique omega and even though we barely know any bits of any of them. Similarly one could base moral arguments off of just the knowledge of the existence of a normative standard against which moral agents could be compared or by which moral agents could in theory be judged; postulating such a standard is itself a non-trivial meta-ethical position.
I’m not sure exactly what point you wish to illustrate with the Chaitin’s omega example. Yes, its value depends on the TM coding. But when a specific one is chosen, the value is unique.
Why so? How well-defined? I find it useful to base normative epistemic arguments off of the existence of Chaitin’s omega, even though there isn’t a unique omega and even though we barely know any bits of any of them. Similarly one could base moral arguments off of just the knowledge of the existence of a normative standard against which moral agents could be compared or by which moral agents could in theory be judged; postulating such a standard is itself a non-trivial meta-ethical position.
I’m not sure exactly what point you wish to illustrate with the Chaitin’s omega example. Yes, its value depends on the TM coding. But when a specific one is chosen, the value is unique.